ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - July 2011 - Volume 17, Issue 03  

Research Article

Topological asymptotic analysis of the Kirchhoff plate bending problem

Amstutz, Samuela1 and Novotny, Antonio A.a2

a1 Laboratoire d'analyse non linéaire et géométrie, Faculté des Sciences, 33 rue Louis Pasteur, 84000 Avignon, France. samuel.amstutz@univ-avignon.fr

a2 Laboratório Nacional de Computação Científica LNCC/MCT, Coordenação de Matemática Aplicada e Computacional, Av. Getúlio Vargas 333, 25651-075 Petrópolis – RJ, Brasil. novotny@lncc.br

Abstract

The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal domain perturbation, like the insertion of holes, inclusions, cracks. In this work we present the calculation of the topological derivative for a class of shape functionals associated to the Kirchhoff plate bending problem, when a circular inclusion is introduced at an arbitrary point of the domain. According to the literature, the topological derivative has been fully developed for a wide range of second-order differential operators. Since we are dealing here with a forth-order operator, we perform a complete mathematical analysis of the problem.

(Received October 16 2009)

(Revised February 15 2010)

(Online publication March 31 2010)

Key Words:

  • Topological sensitivity;
  • topological derivative;
  • topology optimization;
  • Kirchhoff plates

Mathematics Subject Classification:

  • 35J30;
  • 49Q10;
  • 49Q12;
  • 74K20;
  • 74P15